140 LearnersLast updated on May 26th, 2025
Factors of 1414
Factors are the numbers that divide any given number evenly without remainder. In daily life, we use factors for tasks like sharing items equally, arranging things, etc. In this topic, we will learn about the factors of 1414, how they are used in real life, and tips to learn them quickly.
What are the Factors of 1414?
The numbers that divide 1414 evenly are known as factors of 1414.
A factor of 1414 is a number that divides the number without remainder.
The factors of 1414 are 1, 2, 7, 14, 101, 202, 707, and 1414.
Negative factors of 1414: -1, -2, -7, -14, -101, -202, -707, and -1414.
Prime factors of 1414: 2, 7, and 101.
Prime factorization of 1414: 2 × 7 × 101.
The sum of factors of 1414: 1 + 2 + 7 + 14 + 101 + 202 + 707 + 1414 = 2448
How to Find Factors of 1414?
Factors can be found using different methods. Mentioned below are some commonly used methods:
- Finding factors using multiplication
- Finding factors using division method
- Prime factors and Prime factorization
Finding Factors Using Multiplication
To find factors using multiplication, we need to identify the pairs of numbers that are multiplied to give 1414. Identifying the numbers which are multiplied to get the number 1414 is the multiplication method.
Step 1: Multiply 1414 by 1, 1414 × 1 = 1414.
Step 2: Check for other numbers that give 1414 after multiplying
2 × 707 = 1414
7 × 202 = 1414
14 × 101 = 1414
Therefore, the positive factor pairs of 1414 are: (1, 1414), (2, 707), (7, 202), (14, 101).
All these factor pairs result in 1414.
For every positive factor, there is a negative factor.
Finding Factors Using Division Method
Dividing the given number with whole numbers until the remainder becomes zero and listing out the numbers which result as whole numbers as factors. Factors can be calculated by following a simple division method
Step 1: Divide 1414 by 1, 1414 ÷ 1 = 1414.
Step 2: Continue dividing 1414 by the numbers until the remainder becomes 0.
1414 ÷ 1 = 1414
1414 ÷ 2 = 707
1414 ÷ 7 = 202
1414 ÷ 14 = 101
Therefore, the factors of 1414 are: 1, 2, 7, 14, 101, 202, 707, 1414.
Prime Factors and Prime Factorization
The factors can be found by dividing it with prime numbers. We can find the prime factors using the following methods:
- Using prime factorization
- Using factor tree
Using Prime Factorization: In this process, prime factors of 1414 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
1414 ÷ 2 = 707
707 ÷ 7 = 101
101 ÷ 101 = 1
The prime factors of 1414 are 2, 7, and 101.
The prime factorization of 1414 is: 2 × 7 × 101.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 1414 is divided by 2 to get 707.
Step 2: Now divide 707 by 7 to get 101.
Step 3: Here, 101 is a prime number and cannot be divided anymore.
So, the prime factorization of 1414 is: 2 × 7 × 101.
Factor Pairs: Two numbers that are multiplied to give a specific number are called factor pairs. Both positive and negative factors constitute factor pairs.
Positive factor pairs of 1414: (1, 1414), (2, 707), (7, 202), (14, 101).
Negative factor pairs of 1414: (-1, -1414), (-2, -707), (-7, -202), (-14, -101).
Common Mistakes and How to Avoid Them in Factors of 1414
Mistakes are common while finding factors. We can identify and correct those mistakes using the following common mistakes and the ways to avoid them.
Mistake 1
Forgetting the number itself and 1 is a factor
Children might forget to add the given number itself and 1 as a factor. The number itself and 1 are the factors for every number. Always remember to include 1 and the number itself.
For example, in factors of 1414, 1 and 1414 are also factors.
Mistake 2
Missing Negative Factors
We have used only to mention positive factors every time. There are also negative factors, always check whether you have mentioned negative factors.
For example, the factors of 1414 consist of -1, -2, -7, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions also as factors. Only whole numbers can be factors.
For example, thinking 1.5 as a factor, because 1414/1.5 ≈ 942.67, and it is not a whole number.
Mistake 4
Confusing Factors With Prime Numbers
Remember that factors can be any whole numbers, not only just primes.
For example, thinking all the factors of 1414 are prime numbers.
For example, 2, 7, and 101 are the prime factors of 1414, but it has other factors like 14, 202.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 1414 as 2 × 7 × 101 and missing all the key factors.
Factors of 1414 Examples
Problem 1
There are 14 guests and 1414 candies. How will they divide it equally?
They will get 101 candies each.
Explanation
To divide the candies equally, we need to divide the total candies by the number of guests.
1414/14 = 101
Problem 2
A conference room is rectangular, the length of the room is 14 meters, and the total area is 1414 square meters. Find the width.
101 meters.
Explanation
To find the width of the room, we use the formula,
Area = length × width
1414 = 14 × width
To find the value of width, we need to shift 14 to the left side.
1414/14 = width
Width = 101.
Problem 3
There are 707 boxes and 1414 marbles. How many marbles will be in each box?
Each box will have 2 marbles.
Explanation
To find the marbles in each box, divide the total marbles by the number of boxes.
1414/707 = 2
Problem 4
In a class, there are 1414 students, and 101 teams. How many students are there in each team?
There are 14 students in each team.
Explanation
Dividing the students by the total teams, we will get the number of students in each team.
1414/101 = 14
Problem 5
1414 books need to be arranged in 7 shelves. How many books will go on each shelf?
Each of the shelves has 202 books.
Explanation
Divide total books by shelves.
1414/7 = 202
FAQs on Factors of 1414
1.What are the factors of 1414?
2.Mention the prime factors of 1414.
3.Is 1414 a multiple of 14?
4.Mention the factor pairs of 1414?
5.What is the square of 1414?
6.How can children in Canada use numbers in everyday life to understand Factors of 1414?
7.What are some fun ways kids in Canada can practice Factors of 1414 with numbers?
8.What role do numbers and Factors of 1414 play in helping children in Canada develop problem-solving skills?
9.How can families in Canada create number-rich environments to improve Factors of 1414 skills?
Important Glossaries for Factor of 1414
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1414 are 1, 2, 7, 14, 101, 202, 707, and 1414.
- Prime factors: The factors which are prime numbers. For example, 2, 7, and 101 are prime factors of 1414.
- Factor pairs: Two numbers in a pair that are multiplied to give the original number are called factor pairs. For example, the factor pairs of 1414 are (1, 1414), (2, 707), etc.
- Prime factorization: The process of expressing a number as a product of its prime factors. For example, the prime factorization of 1414 is 2 × 7 × 101.
- Negative factors: Factors that are negative numbers, dividing the original number without a remainder. For example, -1, -2, -7, etc., are negative factors of 1414.
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Hiralee Lalitkumar Makwana
About the Author
Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.
Fun Fact
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